Understanding Absolute Value Functions

What is the definition of an absolute value function?

• A function that only accepts positive numbers.

• A function that returns the square of a number.

• A function that outputs the original number without any changes.

• An absolute value function is a function that returns the non-negative value of a number, defined as |x|.

How does the graph of y = |x| look like?

• The graph of y = |x| is a V-shape with a vertex at the origin.

• The graph of y = |x| is a parabola opening downwards.

• The graph of y = |x| is a circle centered at the origin.

• The graph of y = |x| is a straight line.

What are the key features of the graph of an absolute value function?

• Key features include a V-shape, symmetry about the vertex, a minimum point at the vertex, and defined for all real numbers.

• Only defined for positive numbers

• A U-shape that opens downwards

• A straight line with no vertex

How do you find the vertex of the function y = |x - 3| + 2?

• (2, 3)

• (4, 2)

• (3, 3)

• (3, 2)

What transformations occur in the function y = -|x| + 4?

• Vertical shift downwards by 4 units

• Reflection across the x-axis and a vertical shift upwards by 4 units.

• Horizontal shift to the right by 4 units

• Reflection across the y-axis and a vertical shift downwards by 4 units

How do you determine the domain and range of the function y = |x + 1|?

• Domain: (-∞, ∞), Range: [0, ∞)

• Domain: (-∞, 0), Range: [1, ∞)

• Domain: (-1, 1), Range: [0, 1)

• Domain: [0, ∞), Range: (-∞, ∞)

What is the effect of changing the coefficient in y = a|x|?

• The coefficient 'a' affects the horizontal shift of the graph.

• The coefficient 'a' changes the color of the graph.

• The coefficient 'a' affects the vertical stretch/compression and direction of the graph.

• The coefficient 'a' determines the x-intercepts of the graph.

How do you solve the equation |x - 5| = 3 graphically?

• x = 0 and x = 10

• x = 4 and x = 6

• x = 2 and x = 8

• x = 1 and x = 9

What is the relationship between the slopes of the lines in the graph of y = |x|?

• The slopes are 1 and 0.

• The slopes are 1 and -1.

• The slopes are 0 and 1.

• The slopes are 2 and -2.

How can you represent the absolute value function using piecewise notation?

• |x| = { -x, if x >= 0; x, if x < 0 }

• |x| = { 0, if x >= 0; x, if x < 0 }

• |x| = { x, if x < 0; -x, if x >= 0 }

• |x| = { x, if x >= 0; -x, if x < 0 }